Finite Group Databasebeta

← C47×#24625 #26064323

Subgroups — C47×#24625 #26064323

Order 12032.

696 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3094C211yesmaximal, characteristic
2C2×C47×#482C211yesmaximal, characteristic
3C47×#2924C211yesmaximal, characteristic, complemented
4C47×#2911C211yesmaximal, characteristic, complemented
5C47×#2090C211yesmaximal, characteristic, complemented
6C47×#2089C211yesmaximal, characteristic, complemented
7C47×#2063C211yesmaximal, characteristic, complemented
8C47×#2063C211yesmaximal, characteristic, complemented
9C47×#1952C211yesmaximal, characteristic, complemented
10C47×#1951C211yesmaximal, characteristic, complemented
11C47×#1931C211yesmaximal, characteristic, complemented
12C47×#1931C211yesmaximal, characteristic, complemented
13C47×#1900C211yesmaximal, characteristic
14C47×#1855C211yesmaximal, characteristic, complemented
15C47×#1822C211yesmaximal, characteristic, complemented
16C22×M16×C47C2211yescharacteristic
17C2×#121×C47C2211yescharacteristic
18C2×#117×C47C2211yescharacteristic
19C2×#117×C47C2211yescharacteristic
20C47×#482—21no—
21C47×#482—21no—
22C47×#482—21no—
23C47×#482—21no—
24C47×#482—21no—
25C47×#482—21no—
26C47×#481—21no—
27C47×#480—21no—
28C47×#433—21no—
29C47×#433—21no—
30C47×#432—21no—
31C47×#431—21no—
32C2×#108×C47C2211yescharacteristic
33C2×#108×C47C2211yescharacteristic
34C47×#428—21no—
35C47×#428—21no—
36C47×#428C2211yescharacteristic
37C47×#428C2211yescharacteristic
38C47×#428C2211yescharacteristic
39C47×#428C2211yescharacteristic
40C47×#428C2211yescharacteristic
41C47×#428C2211yescharacteristic
42C47×#427—21no—
43C47×#427—21no—
44C2×#107×C47C2211yescharacteristic
45C2×#106×C47C2211yescharacteristic
46C47×#424C2211yescharacteristic
47C47×#424C2211yescharacteristic
48C47×#418C2211yescharacteristic
49C47×#418C2211yescharacteristic
50C2×#102×C47C2211yescharacteristic
51C2×#102×C47C2211yescharacteristic
52C2×#100×C47C2211yescharacteristic
53C2×#100×C47C2211yescharacteristic
54C47×#407C2211yescharacteristic
55C47×#407C2211yescharacteristic
56C2×C22⋊C8×C47C2211yescharacteristic
57C47×#405C2211yescharacteristic
58C47×#405C2211yescharacteristic
59C47×#343C2211yescharacteristic
60C47×#343C2211yescharacteristic
61C47×#343C2211yescharacteristic
62C47×#343C2211yescharacteristic
63C47×#343C2211yescharacteristic
64C47×#343C2211yescharacteristic
65C47×#341C2211yescharacteristic
66C47×#341C2211yescharacteristic
67C22×D4×C47—21no—
68C22×D4×C47C2311yescharacteristic
69C23×C4×C47C2311yescharacteristic
70C2×M16×C47—21no—
71C2×M16×C47—22no—
72C2×M16×C47—22no—
73C2×M16×C47C2311yescharacteristic
74C2×M16×C47C2311yescharacteristic
75C2×M16×C47C2311yescharacteristic
76C2×M16×C47C2311yescharacteristic
77C2×M16×C47C2311yescharacteristic
78C2×M16×C47C2311yescharacteristic
79C22×C8×C47—21no—
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82#121×C47—21no—
83#121×C47—21no—
84#121×C47—21no—
85#121×C47—21no—
86#117×C47—21no—
87#117×C47—21no—
88#117×C47—21no—
89#117×C47—21no—
90#117×C47—21no—
91#117×C47—21no—
92#117×C47D411yescharacteristic
93#117×C47D411yescharacteristic
94#117×C47C2311yescharacteristic
95#117×C47C2311yescharacteristic
96C2×C4⋊C4×C47D411yescharacteristic
97C2×C4⋊C4×C47D411yescharacteristic
98C2×C4⋊C4×C47C2311yescharacteristic
99C2×C4⋊C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C22⋊C4×C47—21no—
102C2×C22⋊C4×C47—21no—
103C2×C22⋊C4×C47—21no—
104C2×C42×C47—21no—
105C2×C42×C47—21no—
106#108×C47—22no—
107#108×C47—22no—
108#107×C47—21no—
109#107×C47—21no—
110#107×C47—21no—
111#107×C47—21no—
112#107×C47—21no—
113#107×C47—21no—
114#107×C47—21no—
115#107×C47—21no—
116#106×C47—21no—
117#106×C47—21no—
118#106×C47—21no—
119#106×C47—21no—
120#106×C47—21no—
121#106×C47—21no—
122#106×C47—21no—
123#106×C47—21no—
124C4⋊C8×C47—21no—
125C4⋊C8×C47—21no—
126C4⋊C8×C47—21no—
127C4⋊C8×C47—21no—
128#102×C47—21no—
129#102×C47—21no—
130#102×C47—21no—
131#102×C47—21no—
132#102×C47—21no—
133#102×C47—21no—
134#102×C47—21no—
135#102×C47—21no—
136#100×C47—22no—
137#100×C47—22no—
138C22⋊C8×C47—21no—
139C22⋊C8×C47—21no—
140C22⋊C8×C47—21no—
141C22⋊C8×C47—21no—
142C22⋊C8×C47D411yescharacteristic
143C22⋊C8×C47D411yescharacteristic
144C22⋊C8×C47D411yescharacteristic
145C22⋊C8×C47D411yescharacteristic
146#97×C47—21no—
147#97×C47—21no—
148C4×C8×C47—21no—
149C4×C8×C47—21no—
150C24×C47—21no—
151C24×C47#4111yescharacteristic
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—41no—
159C2×D4×C47—41no—
160C2×D4×C47—82no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47C2×D411yescharacteristic
171C22×C4×C47C2×D411yescharacteristic
172C22×C4×C47C2×D411yescharacteristic
173C22×C4×C47C2×D411yescharacteristic
174C22×C4×C47#4111yescharacteristic
175C22×C4×C47C2411yescharacteristic
176M16×C47—24no—
177M16×C47—21no—
178M16×C47—21no—
179M16×C47—21no—
180M16×C47—21no—
181M16×C47—21no—
182M16×C47—21no—
183M16×C47—21no—
184M16×C47—21no—
185M16×C47—21no—
186M16×C47—21no—
187M16×C47#4112yes—
188M16×C47#4112yes—
189C2×C8×C47—24no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47C2×D411yescharacteristic
201C2×C8×C47C2×D411yescharacteristic
202C2×C8×C47C2×D411yescharacteristic
203C2×C8×C47C2×D411yescharacteristic
204C4⋊C4×C47—21no—
205C4⋊C4×C47—21no—
206C4⋊C4×C47—21no—
207C4⋊C4×C47—21no—
208C4⋊C4×C47—21no—
209C4⋊C4×C47—21no—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—21no—
212C4⋊C4×C47C2×D411yescharacteristic
213C4⋊C4×C47C2×D411yescharacteristic
214C4⋊C4×C47C2×D411yescharacteristic
215C4⋊C4×C47C2×D411yescharacteristic
216C22⋊C4×C47—21no—
217C22⋊C4×C47—21no—
218C22⋊C4×C47—21no—
219C22⋊C4×C47—21no—
220C22⋊C4×C47—41no—
221C22⋊C4×C47—41no—
222C22⋊C4×C47—41no—
223C22⋊C4×C47—41no—
224C42×C47—21no—
225C42×C47—21no—
226C42×C47—21no—
227C42×C47—21no—
228C42×C47—41no—
229C42×C47—41no—
230C23×C47—21no—
231C23×C47—21no—
232C23×C47—41no—
233C23×C47—41no—
234C23×C47—41no—
235C23×C47—41no—
236C23×C47—41no—
237C23×C47—81no—
238C23×C47—81no—
239C23×C47#12111yescharacteristic
240C23×C47#12111yescharacteristic
241C23×C47C2×#4111yescharacteristic
242D4×C47—41no—
243D4×C47—41no—
244D4×C47—41no—
245D4×C47—41no—
246D4×C47—82no—
247D4×C47—82no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—42no—
263C2×C4×C47—41no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47—81no—
267C2×C4×C47—81no—
268C2×C4×C47—81no—
269C2×C4×C47—81no—
270C2×C4×C47#12111yescharacteristic
271C2×C4×C47#12111yescharacteristic
272C2×C4×C47C22×D411yescharacteristic
273C2×C4×C47C22×D411yescharacteristic
274C2×C4×C47C2×#4111yescharacteristic
275C2×C4×C47C2×#4111yescharacteristic
276C2×C4×C472−1+411yescharacteristic
277C2×C4×C472−1+411yescharacteristic
278C8×C47—22no—
279C8×C47—22no—
280C8×C47—21no—
281C8×C47—21no—
282C8×C47—21no—
283C8×C47—21no—
284C8×C47—41no—
285C8×C47—41no—
286C8×C47—41no—
287C8×C47—41no—
288#24625C4711yesmaximal, characteristic, direct product factor, Sylow
289C22×C47—21no—
290C22×C47—21no—
291C22×C47—21no—
292C22×C47—21no—
293C22×C47—21no—
294C22×C47—21no—
295C22×C47—21no—
296C22×C47—21no—
297C22×C47—81no—
298C22×C47—81no—
299C22×C47—81no—
300C22×C47—81no—
301C22×C47—81no—
302C22×C47—161no—
303C22×C47—161no—
304C22×C47C2×#12111yescharacteristic
305C22×C47#55211yescharacteristic
306C22×C47#55211yescharacteristic
307C4×C47—21no—
308C4×C47—21no—
309C4×C47—41no—
310C4×C47—41no—
311C4×C47—41no—
312C4×C47—41no—
313C4×C47—81no—
314C4×C47—81no—
315C4×C47—81no—
316C4×C47#52511yescharacteristic
317C4×C47#53611yescharacteristic
318C4×C47#54711yescharacteristic
319C4×C47#54711yescharacteristic
320#3094C2×C4711yescharacteristic
321C2×#482C2×C4711yescharacteristic
322#2924C2×C4711yescharacteristic, complemented
323#2911C2×C4711yescharacteristic, complemented
324#2090C2×C4711yescharacteristic, complemented
325#2089C2×C4711yescharacteristic, complemented
326#2063C2×C4711yescharacteristic, complemented
327#2063C2×C4711yescharacteristic, complemented
328#1952C2×C4711yescharacteristic, complemented
329#1951C2×C4711yescharacteristic, complemented
330#1931C2×C4711yescharacteristic, complemented
331#1931C2×C4711yescharacteristic, complemented
332#1900C2×C4711yescharacteristic
333#1855C2×C4711yescharacteristic, complemented
334#1822C2×C4711yescharacteristic, complemented
335C2×C47—21no—
336C2×C47—21no—
337C2×C47—41no—
338C2×C47—41no—
339C2×C47—161no—
340C2×C47#241311yescharacteristic
341C2×C47#306711yescharacteristic
342C2×C47#306811yescharacteristic
343C22×M16C22×C4711yescharacteristic
344C2×#121C22×C4711yescharacteristic
345C2×#117C22×C4711yescharacteristic
346C2×#117C22×C4711yescharacteristic
347#482—21no—
348#482—21no—
349#482—21no—
350#482—21no—
351#482—21no—
352#482—21no—
353#481—21no—
354#480—21no—
355#433—21no—
356#433—21no—
357#432—21no—
358#431—21no—
359C2×#108C22×C4711yescharacteristic
360C2×#108C22×C4711yescharacteristic
361#428—21no—
362#428—21no—
363#428C22×C4711yescharacteristic
364#428C22×C4711yescharacteristic
365#428C22×C4711yescharacteristic
366#428C22×C4711yescharacteristic
367#428C22×C4711yescharacteristic
368#428C22×C4711yescharacteristic
369#427—21no—
370#427—21no—
371C2×#107C22×C4711yescharacteristic
372C2×#106C22×C4711yescharacteristic
373#424C22×C4711yescharacteristic
374#424C22×C4711yescharacteristic
375#418C22×C4711yescharacteristic
376#418C22×C4711yescharacteristic
377C2×#102C22×C4711yescharacteristic
378C2×#102C22×C4711yescharacteristic
379C2×#100C22×C4711yescharacteristic
380C2×#100C22×C4711yescharacteristic
381#407C22×C4711yescharacteristic
382#407C22×C4711yescharacteristic
383C2×C22⋊C8C22×C4711yescharacteristic
384#405C22×C4711yescharacteristic
385#405C22×C4711yescharacteristic
386#343C22×C4711yescharacteristic
387#343C22×C4711yescharacteristic
388#343C22×C4711yescharacteristic
389#343C22×C4711yescharacteristic
390#343C22×C4711yescharacteristic
391#343C22×C4711yescharacteristic
392#341C22×C4711yescharacteristic
393#341C22×C4711yescharacteristic
394C47#2462511yescharacteristic, direct product factor, Sylow
395C22×D4—21no—
396C22×D4C23×C4711yescharacteristic
397C23×C4C23×C4711yescharacteristic
398C2×M16—21no—
399C2×M16—22no—
400C2×M16—22no—
401C2×M16C23×C4711yescharacteristic
402C2×M16C23×C4711yescharacteristic
403C2×M16C23×C4711yescharacteristic
404C2×M16C23×C4711yescharacteristic
405C2×M16C23×C4711yescharacteristic
406C2×M16C23×C4711yescharacteristic
407C22×C8—21no—
408C22×C8C23×C4711yescharacteristic
409C22×C8C23×C4711yescharacteristic
410#121—21no—
411#121—21no—
412#121—21no—
413#121—21no—
414#117—21no—
415#117—21no—
416#117—21no—
417#117—21no—
418#117—21no—
419#117—21no—
420#117D4×C4711yescharacteristic
421#117D4×C4711yescharacteristic
422#117C23×C4711yescharacteristic
423#117C23×C4711yescharacteristic
424C2×C4⋊C4D4×C4711yescharacteristic
425C2×C4⋊C4D4×C4711yescharacteristic
426C2×C4⋊C4C23×C4711yescharacteristic
427C2×C4⋊C4C23×C4711yescharacteristic
428C2×C4⋊C4C23×C4711yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C42—21no—
433C2×C42—21no—
434#108—22no—
435#108—22no—
436#107—21no—
437#107—21no—
438#107—21no—
439#107—21no—
440#107—21no—
441#107—21no—
442#107—21no—
443#107—21no—
444#106—21no—
445#106—21no—
446#106—21no—
447#106—21no—
448#106—21no—
449#106—21no—
450#106—21no—
451#106—21no—
452C4⋊C8—21no—
453C4⋊C8—21no—
454C4⋊C8—21no—
455C4⋊C8—21no—
456#102—21no—
457#102—21no—
458#102—21no—
459#102—21no—
460#102—21no—
461#102—21no—
462#102—21no—
463#102—21no—
464#100—22no—
465#100—22no—
466C22⋊C8—21no—
467C22⋊C8—21no—
468C22⋊C8—21no—
469C22⋊C8—21no—
470C22⋊C8D4×C4711yescharacteristic
471C22⋊C8D4×C4711yescharacteristic
472C22⋊C8D4×C4711yescharacteristic
473C22⋊C8D4×C4711yescharacteristic
474#97—21no—
475#97—21no—
476C4×C8—21no—
477C4×C8—21no—
478C24—21no—
479C24#41×C4711yescharacteristic
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—82no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4C2×D4×C4711yescharacteristic
499C22×C4C2×D4×C4711yescharacteristic
500C22×C4C2×D4×C4711yescharacteristic
501C22×C4C2×D4×C4711yescharacteristic
502C22×C4#41×C4711yescharacteristic
503C22×C4C24×C4711yescharacteristic
504M16—24no—
505M16—21no—
506M16—21no—
507M16—21no—
508M16—21no—
509M16—21no—
510M16—21no—
511M16—21no—
512M16—21no—
513M16—21no—
514M16—21no—
515M16#41×C4712yes—
516M16#41×C4712yes—
517C2×C8—24no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8C2×D4×C4711yescharacteristic
529C2×C8C2×D4×C4711yescharacteristic
530C2×C8C2×D4×C4711yescharacteristic
531C2×C8C2×D4×C4711yescharacteristic
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4C2×D4×C4711yescharacteristic
541C4⋊C4C2×D4×C4711yescharacteristic
542C4⋊C4C2×D4×C4711yescharacteristic
543C4⋊C4C2×D4×C4711yescharacteristic
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C22⋊C4—41no—
551C22⋊C4—41no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—41no—
557C42—41no—
558C23—21no—
559C23—21no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—81no—
566C23—81no—
567C23#121×C4711yescharacteristic
568C23#121×C4711yescharacteristic
569C23C2×#41×C4711yescharacteristic
570D4—41no—
571D4—41no—
572D4—41no—
573D4—41no—
574D4—82no—
575D4—82no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4#121×C4711yescharacteristic
599C2×C4#121×C4711yescharacteristic
600C2×C4C22×D4×C4711yescharacteristic
601C2×C4C22×D4×C4711yescharacteristic
602C2×C4C2×#41×C4711yescharacteristic
603C2×C4C2×#41×C4711yescharacteristic
604C2×C42−1+4×C4711yescharacteristic
605C2×C42−1+4×C4711yescharacteristic
606C8—22no—
607C8—22no—
608C8—21no—
609C8—21no—
610C8—21no—
611C8—21no—
612C8—41no—
613C8—41no—
614C8—41no—
615C8—41no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—21no—
623C22—21no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—161no—
630C22—161no—
631C22C2×#121×C4711yescharacteristic
632C22C47×#55211yescharacteristic
633C22C47×#55211yescharacteristic
634C4—21no—
635C4—21no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—81no—
641C4—81no—
642C4—81no—
643C4C47×#52511yescharacteristic
644C4C47×#53611yescharacteristic
645C4C47×#54711yescharacteristic
646C4C47×#54711yescharacteristic
647C2—21no—
648C2—21no—
649C2—41no—
650C2—41no—
651C2—161no—
652C2C47×#241311yescharacteristic
653C2C47×#306711yescharacteristic
654C2C47×#306811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×#121×C47C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C47×#2924C2semidirect
4. C47×#2911C2semidirect
5. C47×#2090C2semidirect
6. C47×#2089C2semidirect
7. C47×#2063C2semidirect
8. C47×#2063C2semidirect
9. C47×#1952C2semidirect
10. C47×#1951C2semidirect
11. C47×#1931C2semidirect
12. C47×#1931C2semidirect
14. C47×#1855C2semidirect
15. C47×#1822C2semidirect
288. #24625C47direct (N × H)
322. #2924C2×C47semidirect
323. #2911C2×C47semidirect
324. #2090C2×C47semidirect
325. #2089C2×C47semidirect
326. #2063C2×C47semidirect
327. #2063C2×C47semidirect
328. #1952C2×C47semidirect
329. #1951C2×C47semidirect
330. #1931C2×C47semidirect
331. #1931C2×C47semidirect
333. #1855C2×C47semidirect
334. #1822C2×C47semidirect
394. C47#24625direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C47×#30942
C2×C47×#4822
C47×#29242
C47×#29112
C47×#20902
C47×#20892
C47×#20632
C47×#19522
C47×#19512
C47×#19312
C47×#19002
C47×#18552
C47×#18222
#2462547